WO2022227282A1 - 一种磁共振安全的旋转编码器及旋转角度检测方法 - Google Patents

一种磁共振安全的旋转编码器及旋转角度检测方法 Download PDF

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WO2022227282A1
WO2022227282A1 PCT/CN2021/105090 CN2021105090W WO2022227282A1 WO 2022227282 A1 WO2022227282 A1 WO 2022227282A1 CN 2021105090 W CN2021105090 W CN 2021105090W WO 2022227282 A1 WO2022227282 A1 WO 2022227282A1
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strain gauge
point
magnetic resonance
shape
fbg
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高安柱
黄少平
杨广中
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Shanghai Jiao Tong University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00—Arrangements or instruments for measuring magnetic variables
    • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance

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  • the invention relates to the technical field of magnetic resonance, in particular to a magnetic resonance-safe rotary encoder and a rotation angle detection method.
  • Magnetic Resonance Safe Magnetic Resonance Compliant
  • Magnetic Resonance Unsafe the magnetic resonance safety equipment has the highest safety factor and is suitable for all magnetic resonance scenarios. Magnetic resonance compatible products need to be tested for specific scenarios. At present, some magnetic resonance safe/compatible drivers and sensors have been used in practical work. However, magnetic resonance-safe angle sensors are still relatively rare.
  • Optical fiber is a natural magnetic resonance safe device.
  • the prior art adopts the principle of light intensity change in the optical fiber to design a magnetic resonance-safe angle encoder.
  • a certain regular reflection sheet is arranged on the disc, and then the end of the optical fiber is designed to be perpendicular to the reflection sheet, so as to realize the change of the reflected light intensity with or without the reflection sheet.
  • the disadvantage of the prior art is that for a light-intensity encoder, since the intensity of the light will attenuate and fluctuate after long-distance transmission, the stability control of the light source is extremely required. In addition, the external mechanical vibration will also lead to inaccurate alignment of the fiber end, which will lead to fluctuations in light intensity detection.
  • a large number of reflection points need to be set.
  • traditional fiber Bragg grating sensors have a small detection strain range, and existing technologies can only detect rotation angles within a limited range. Therefore, it is necessary to propose a technical solution to improve the above-mentioned technical problems.
  • the purpose of the present invention is to provide a magnetic resonance-safe rotary encoder and a rotation angle detection method.
  • a magnetic resonance safe rotary encoder provided according to the present invention includes a rotating shaft, an eccentric, a bearing, a shaft sleeve, a shape sensing strain gauge, a fiber Bragg grating sensor, a temperature compensation strain gauge, a wedge-shaped groove, a fixed wedge, and a back cover and casing;
  • the rotating shaft is connected with the object to be measured;
  • the eccentric wheel is arranged at the rear end of the rotating shaft, and the rotating shaft drives the eccentric wheel to rotate;
  • the bearing is installed on both sides of the shaft sleeve; the shaft sleeve is worn on the rotating shaft;
  • the shape sensing strain gauge is arranged in contact with the eccentric wheel, and the shape sensing strain gauge and the temperature compensation strain gauge are installed in the wedge-shaped groove, and the fixing wedge is used for fixing the shape sensing strain gauge and the temperature compensation strain gauge;
  • the fiber Bragg grating sensor is installed on the shape sensing strain gauge, and the optical fiber on the fiber Bragg grating sensor is connected to the external grating demodulator through the back cover and the sleeve;
  • the rotating shaft rotates, and the motion trajectory of the contact point between the shape-sensing strain gauge and the eccentric is approximately a sine curve.
  • the present invention also provides a method for detecting a rotation angle of a magnetic resonance-safe rotary encoder, the method includes the above-mentioned magnetic resonance-safe rotary encoder, and the method includes the following steps:
  • Step 1 establish the geometric relationship between the rotation angle ⁇ of the rotating shaft and the coordinates of the contact point P of the shape sensing strain gauge 122 and the eccentric 121;
  • Step 2 using the three-joint pseudo-rigid body model PRB 3R to establish the relationship between the coordinates of point P and the state variable B of the shape-aware strain gauge 122;
  • Step 3 use the chain algorithm to solve the strain of the Bragg grating 125 installed on the shape sensing strain gauge 122;
  • Step 4 From the relationship between the wavelength of the Bragg grating 125 and the strain, obtain the relationship between the acquisition wavelength after temperature compensation and the strain of the actual shape sensing strain gauge 122;
  • Step 5 Through the model established in steps 1-4, design a corresponding matching algorithm for the final angle detection.
  • the eccentric rotates on the xoy plane
  • K is the point where the xoy plane of the eccentric is the farthest from the origin O along the y-axis direction; when the eccentric rotates ⁇ , K moves to K along the circular trajectory ' point, the trajectory is consistent with the moving trajectory of the center Q of the eccentric wheel 121; the kinematics of K is expressed as follows:
  • rc is the eccentric radius
  • D is the diameter of the eccentric
  • K r and K l respectively represent the two points with the largest absolute value of the x-coordinate in the motion trajectory of the K point; K r represents the point whose x-coordinate is a negative number, and K l represents a point whose x-coordinate is a positive number.
  • the width w of the shape sensing strain gauge 122 is greater than the distance between K r and K l , and the shape sensing strain gauge 122 is tangent to the curved surface K S located just above the point K;
  • the P point is the tangent point, and the coordinate of the P point depends on the y coordinate of the K point; the direction of the contact force F is from the center of the curved surface K S to the P point; the kinematics of the P point is expressed as follows:
  • rs is the radius of the curved surface K S
  • ⁇ is the angle between the contact force F and the positive direction of the y-axis.
  • the P changes with the change of ⁇ , and the change of the P point causes the state variable B of the shape sensing strain gauge to change, and the definition of the state variable B is as follows:
  • L represents the length from point H to point P along the beam direction
  • L is the effective length of the shape sensing strain gauge
  • F represents the magnitude of the contact force
  • the state variable B contains three unknown quantities, and three sets of constraint relationships need to be established to solve the three unknown quantities;
  • ⁇ is the deflection angle of the shape-sensing strain gauge 122, and the tangent relationship between the shape-sensing strain gauge 122 and the curved surface K S , the first set of constraints is obtained as:
  • the a and b represent the projection of the beam on the y and z axes, respectively:
  • ⁇ i represents the i-th pseudo-rigid body characteristic parameter
  • ⁇ p,i represents the i-th pseudo-rigid body joint angle
  • the coordinates of the fixed point H are [0,H y ,H z ] T ;
  • the y and z coordinates of P are represented by pseudo rigid body parameters as:
  • k i is the stiffness coefficient of the pseudo-rigid body joint
  • F y and F z represent the projection of the contact force F on the y-axis and z-axis
  • J T is the Jacobian matrix represented by the pseudo-rigid body parameters.
  • the total deflection angle of the FBG Solve by the following formula:
  • the strain ⁇ of the FBG is obtained by the deflection angle Solve;
  • FBG125 is installed in the groove of the strain gauge, and the distance between the centerline of the FBG and the centerline of the beam is defined as h;
  • the strain of the FBG is expressed as follows:
  • the Bragg wavelength of the grating is:
  • n eff is the effective refractive index of the light propagation mode
  • ⁇ is the grating period
  • the wavelength change ⁇ is determined by the strain ⁇ and the temperature T, and the relationship is:
  • ⁇ ⁇ is the elastic optical coefficient of the fiber material
  • ⁇ 0 is the center wavelength
  • ⁇ T is the temperature change.
  • the wavelength change of the temperature-compensated FBG is substituted into the strain FBG to obtain:
  • ⁇ T is the wavelength change of the temperature-compensated FBG; the superscript i represents the parameter value of the ith strained FBG.
  • the present invention has the following beneficial effects:
  • the present invention converts the rotation angle of the rotating shaft into the deformation of the shape sensing strain gauge by adopting the structure of the eccentric wheel and the shape sensing strain gauge; it solves the problem that the measurement range of the traditional FBG-based detection method is too small to detect 360° rotation.
  • the problem of angle; and, the structure can be assembled with magnetically safe materials such as resin/PMMA, etc., so as to achieve the characteristics of magnetic resonance safety;
  • the present invention solves the problem that the state variable of the beam is difficult to be solved by the traditional integral method when the length of the beam is variable by adopting the modeling method of the pseudo-rigid body and introducing three sets of constraint relations.
  • the mapping from the rotation angle to the wavelength change of the FBG is realized; the experiments show that the overall detection accuracy of the device is 1.6°; the root mean square error is 0.46°.
  • Fig. 1 is the overall structure diagram of the present invention
  • FIG. 2 is a structural diagram of the FBG shape sensing strain gauge of the present invention.
  • Fig. 3 is the contact mode diagram of the shape sensing strain gauge of the present invention and the eccentric;
  • FIG. 5 is a schematic diagram of a pseudo-rigid body model of the shape sensing strain gauge of the present invention.
  • Fig. 6 is the chain algorithm node segmentation diagram of the present invention.
  • FIG. 7 is a schematic diagram of the FBG detection of the present invention.
  • FIG. 1 shows an overall configuration diagram of the angle sensor.
  • the rotating shaft 101 is connected with the object to be tested, and the rotation of the eccentric wheel 121 is driven by the rotation of the rotating shaft 101 .
  • Two ceramic bearings 102 are installed on both sides of the shaft sleeve 111 to ensure the stability of the rotating shaft 101 .
  • the two shape sensing strain gauges 122 are in contact with the edge of the eccentric 121 . Therefore, when the shaft 101 rotates, the contact point will change, and then the strain size of the shape sensing strain gauge 122 will change accordingly.
  • the fiber Bragg grating sensor 124 is installed in the middle of the shape sensing strain gauge 122.
  • the sensor 124 When the shape sensing strain gauge 122 is deflected, the sensor 124 is synchronously strained, and the wavelength of the light detected by the sensor will change.
  • the contact relationship between the shape sensing strain gauge 122 and the eccentric wheel 121 can be in various forms, as shown in FIG. 3 , one is vertical contact and the other is tangential contact.
  • the shape sensing strain gauge 122 and the temperature compensation strain gauge 123 are installed in the wedge groove 104 and fixed by the fixing wedge 103 .
  • the optical fiber 124 is connected to the external grating demodulator through the back cover 114 through the sleeve 105 .
  • the motion trajectory of the contact point P between the shape sensing strain gauge 122 and the eccentric wheel 121 can be approximated as a sinusoid. Since any amplitude of the sinusoid in one cycle corresponds to two rotation angles, the amplitude is consistent with the strain of the shape sensing strain gauge 122 . Therefore, it is necessary to detect at least the strain magnitudes of the shape sensing strain gauges 122 at two different positions to determine the current rotation angle.
  • the present invention uses a 120° distribution method to design the relative positional relationship between the two shape-sensing strain gauges.
  • the positional relationship of other shape-sensing strain gauges or the installation of more than two shape-sensing strain gauges is also consistent with the idea proposed by the invention.
  • the fiber Bragg grating sensor 124 is extremely sensitive to temperature.
  • a temperature compensation strain gauge 123 that is not in contact with the eccentric is designed to be 120° from the other two shape sensing strain gauges 122.
  • the circumferential distribution relationship of the interval, the direction is the same as the axial direction.
  • the detected wavelength values of the sensors 124 in the two shape-sensing strain gauges 122 can correspond one-to-one with the rotation angle of the shaft.
  • Piezoelectric sensors or other sensors that can detect the deformation of the beam can also be used for the strain detection method of the shape sensing strain gauge.
  • the overall modeling idea is as follows: first, the geometric relationship between the rotation angle ⁇ of the shaft 101 and the coordinates of point P (the contact point between the shape-aware strain gauge 122 and the eccentric 121 ) is established; secondly, a three-joint pseudo-rigid body model (PRB 3R ) to establish the relationship between the coordinates of point P and the state variable B of the shape-sensing strain gauge 122; then use the chain algorithm to solve the strain of the Bragg grating (FBG) 125 installed at a specific position of the shape-sensing strain gauge 122; From the relationship between wavelength and strain, the relationship between the acquisition wavelength after temperature compensation and the strain of the actual shape sensing strain gauge 122 can be obtained. Through the model established above, a corresponding matching algorithm is designed for the final angle detection.
  • PRB 3R pseudo-rigid body model
  • FIG. 4 shows the geometric relationship between the eccentric 121 and the shape sensing strain gauge 122 .
  • the eccentric rotates on the xoy plane, as shown in Fig. 4(a).
  • K is the point on the xoy plane of the eccentric that is farthest from the origin O along the y-axis.
  • K moves to the point K' along a circular trajectory, which is consistent with the movement trajectory of the center Q of the eccentric wheel 121 . Therefore, the kinematics of K can be expressed as follows:
  • the two farthest points K r and K l are defined to represent the two points with the largest absolute value of the x-coordinate in the motion trajectory of the K point, respectively.
  • K r represents a point with a negative x coordinate
  • K l represents a point with a positive x coordinate.
  • rs is the radius of the curved surface K S
  • ⁇ is the angle between the contact force F and the positive direction of the y-axis.
  • L represents the length along the beam direction from point H to point P in Fig. 4(b), which is the effective length of the shape sensing strain gauge.
  • F represents the magnitude of the contact force.
  • the FBG is installed at point M shown in Figure 4(b), and its length is l.
  • d is the distance from point H to point M along the beam.
  • the traditional beam theory is mostly used to analyze the beam state determined by L, and L in this model is a variable, so it is difficult to directly use the traditional beam theory to solve the strain at the location M of the FBG.
  • the present invention decomposes the problem into two steps: 1) first, a three-joint pseudo-rigid body model is used to establish the corresponding relationship between the state variables B and P; 2) a chain algorithm is used to solve the strain value.
  • FIG. 5 shows a three-joint pseudo-rigid body model of the shape-aware strain gauge 122 .
  • ⁇ is defined as the deflection angle of the shape sensing strain gauge 122 as shown in FIG. 5 . Due to the tangent relationship between the shape-aware strain gauge 122 and the curved surface K S , the first set of constraint relationships can be obtained as:
  • a and b are the projections of the beam on the y and z axes, respectively:
  • ⁇ i represents the i-th pseudo-rigid body characteristic parameter
  • ⁇ p,i represents the i-th pseudo-rigid body joint angle.
  • the coordinates of the fixed point H are [0, Hy, Hz]T. Therefore, the y,z coordinates of P can be expressed in pseudo-rigid body parameters as follows:
  • the state variable B can be solved by the following equation:
  • k i is the stiffness coefficient of the pseudo-rigid body joint
  • F y and F z represent the projections of the contact force F on the y- and z-axes.
  • J T is the Jacobian matrix represented by pseudo-rigid body parameters. Since (8) contains a variety of sine functions, it is difficult to directly obtain an analytical solution. The problem is solved using the MATLAB numerical solution algorithm "fsolve".
  • MS and ME represent the start node and end node of FBG, the start node represents the node closest to H , and vice versa, the end node represents the farthest point.
  • the strain ⁇ of the FBG can be obtained by solving the deflection angle of (9) to solve.
  • Figure 7(a) represents the strain schematic of the FBG. Because the force acting on the beam is a side contact force, the axial force of the shape-aware strain gauge can be ignored. Therefore, it can be assumed that the centerline length of the shape-aware strain gage is constant. As shown in Fig. 7(a), the FBG125 is installed in the groove of the shape-sensing strain gauge, and the distance between the centerline of the FBG and the centerline of the beam is defined as h. Therefore, the strain of the FBG can be expressed as follows:
  • the Bragg wavelength of the grating is:
  • n eff is the effective refractive index of the light propagation mode
  • ⁇ is the grating period.
  • the change in wavelength ⁇ is determined by the strain ⁇ and the temperature T, and the relationship is:
  • ⁇ ⁇ is the elastic-optical coefficient of the fiber material, and its value is 0.216; ⁇ 0 is the center wavelength, which corresponds to the reflection wavelength of the fiber in the straight state; ⁇ T is the temperature change.
  • the strain ⁇ in formula (13) is 0, and the wavelength change of the temperature-compensated FBG is substituted into the strain FBG to obtain:
  • ⁇ T is the wavelength change of the temperature-compensated FBG; the superscript i represents the parameter value of the i-th strained FBG.
  • the two FBGs have a phase difference of 120°, so the wavelength of the two is between the rotation angle of the shaft.
  • the relationship curve is shown in Figure 7(b).
  • the corresponding wavelength data is detected by the FBG modem, and the rotation angle ⁇ of the shaft can be uniquely determined through the mapping relationship between the wavelength and the angle shown in Fig. 7(b).
  • the invention converts the rotation angle of the rotating shaft into the deformation of the shape sensing strain gauge by adopting the structure of the eccentric wheel and the shape sensing strain gauge; problem; and, the structure can be assembled with magnetically safe materials such as resin/PMMA, etc., so as to realize the magnetic resonance safety characteristics.
  • the present invention solves the problem that the state variable of the beam is difficult to be solved by the traditional integral method when the length of the beam is variable by adopting the modeling method of the pseudo-rigid body and introducing three sets of constraint relations, thereby realizing The mapping of the rotation angle to the wavelength change of the FBG; experiments show that the overall detection accuracy of the device is 1.6°; the root mean square error is 0.46°.
  • the system provided by the present invention and its various devices can be implemented by logically programming the method steps. , modules, and units realize the same function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system provided by the present invention and its various devices, modules and units can be regarded as a kind of hardware components, and the devices, modules and units included in it for realizing various functions can also be regarded as hardware components.
  • the device, module and unit for realizing various functions can also be regarded as both a software module for realizing the method and a structure within a hardware component.

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  • Condensed Matter Physics & Semiconductors (AREA)
  • General Physics & Mathematics (AREA)
  • Measurement Of Length, Angles, Or The Like Using Electric Or Magnetic Means (AREA)
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Abstract

一种磁共振安全的旋转编码器，包括旋转轴(101)、偏心轮(121)、轴承(102)、轴套(111)、形状感知应变片(122)、光纤布拉格光栅传感器(124)、温度补偿应变片(123)、楔形槽(104)、固定楔子(103)、后盖(114)和套管(105)；旋转轴(101)与待测物相连接；偏心轮(121)穿设在旋转轴(101)尾端，旋转轴(101)带动偏心轮(121)旋转；轴承(102)安装在轴套(111)的两侧；轴套(111)穿设在旋转轴(101)上；形状感知应变片(122)与偏心轮(121)接触设置，形状感知应变片(122)和温度补偿应变片(123)安装在楔形槽(104)，固定楔子(103)用于固定形状感知应变片(122)和温度补偿应变片(123)；光纤布拉格光栅传感器(124)安装在形状感知应变片(122)上，解决了传统基于FBG的检测方法的测量范围太小，无法检测360°旋转角度的问题；此外，该结构便于用磁共振安全的材料制作，实现编码器的磁共振安全特性。

Description

一种磁共振安全的旋转编码器及旋转角度检测方法 技术领域
本发明涉及磁共振的技术领域，具体地，涉及一种磁共振安全的旋转编码器及旋转角度检测方法。
背景技术
随着磁共振成像技术在硬件及算法方面的日趋成熟，近年来它用于机器人介入手术的实时导航方面的潜力引起了越来越多的关注。相比于传统的CT、PET及超声成像，磁共振无电离辐射，并且有着更加丰富的软组织信息，还可以用于温度、动态血流检测。近年来，MRI引导的手术机器人也推陈出新，表现出巨大的临床潜力。它相比医生的操作，有着高精度、高可靠、易操作等优点。然而，磁共振环境下，传统的设备涉及到磁兼容问题难以被应用。要求每个零部件都能在磁共振的环境下正常工作。美国测试与材料学会将用于该环境下的设备分为三个等级：磁共振安全；磁共振兼容；磁共振不安全。其中磁共振安全的设备，安全系数最高，适用于所有的磁共振场景。而磁共振兼容的产品需要针对特定的场景进行测试。目前，部分磁共振安全/兼容的驱动器、传感器已经被应用于实际工作中。但是磁共振安全的角度传感器仍然较为稀少。
磁共振安全的旋转角编码器的技术难点在于寻找一种磁共振安全的角度检测方法。传统的采用光电效应、电阻变化的方法将不再适用。光纤是一种天然的磁共振安全的器件。为此，现有技术采用光纤内光强变化的原理来设计磁共振安全的角度编码器。该装置通过在圆盘上设置一定规律的反射片，再设计光纤末端与反射片垂直，从而实现有无反射片情况下的反射光强变化。
现有技术的不足之处是：对于光强式的编码器，由于光经过长距离传输后，光的强度会衰减、波动，因此对光源的稳定性控制要求极高。且外部的机械振动也会导致光纤末端对位不准，进而导致光强检测产生波动。并且，由于加工技术的限制，要实现高精度的检测，需要设置大量的反射点。而小尺寸的传感器由于空间有限，难以加工大量刻槽，从而难以达到高精度检测。最后，传统的光纤布拉格光栅传感 器的检测应变范围较小，现有的技术只能检测有限范围内的旋转角度。因此，需要提出一种技术方案以改善上述技术问题。
发明内容
针对现有技术中的缺陷，本发明的目的是提供一种磁共振安全的旋转编码器及旋转角度检测方法。
根据本发明提供的一种磁共振安全的旋转编码器，包括旋转轴、偏心轮、轴承、轴套、形状感知应变片、光纤布拉格光栅传感器、温度补偿应变片、楔形槽、固定楔子、后盖和套管；
所述旋转轴与待测物相连接；所述偏心轮穿设在旋转轴尾端，并由旋转轴带动偏心轮旋转；
所述轴承安装在轴套的两侧；所述轴套穿设在旋转轴上；
所述形状感知应变片与偏心轮接触设置，且所述形状感知应变片和温度补偿应变片安装在楔形槽，所述固定楔子用于固定形状感知应变片和温度补偿应变片；
所述光纤布拉格光栅传感器安装在形状感知应变片上，所述光纤布拉格光栅传感器上的光纤经过后盖穿过套管与外部光栅解调器相连接；
所述旋转轴发生旋转，形状感知应变片与偏心轮的接触点的运动轨迹近似为正弦曲线。
本发明还提供一种磁共振安全的旋转编码器的旋转角度检测方法，所述方法包括上述中的一种磁共振安全的旋转编码器，所述方法包括如下步骤：
步骤1：建立旋转轴的旋转角θ与形状感知应变片122与偏心轮121的接触点P点坐标的几何关系；
步骤2：采用三关节伪刚体模型PRB 3R建立P点坐标与形状感知应变片122的状态变量B之间的关系；
步骤3：采用链式算法求解安装在形状感知应变片122上的布拉格光栅125的应变；
步骤4：由布拉格光栅125的波长与应变的关系，得到经过温度补偿后的采集波长与实际形状感知应变片122的应变之间的关系；
步骤5：通过步骤1-4建立的模型，设计相应的匹配算法用于最终的角度检测。
优选地，所述偏心轮在xoy平面上旋转，K是偏心轮的xoy平面沿着y轴方向与原点O距离最远的点；当偏心轮旋转θ时，K沿着圆形轨迹移动到K'点，该轨迹与 偏心轮121的中心Q的移动轨迹一致；K的运动学表示为如下：
K＝[-r ccosθ,r csinθ+D/2,0] T
其中，r c是偏心半径，D是偏心轮的直径；
所述K r和K l分别表示K点的运动轨迹中的x坐标绝对值最大的两个点；K r表示x坐标为负数的点，K l表示x坐标为正数的点。
优选地，所述形状感知应变片122的宽度w大于K r和K l之间的距离，形状感知应变片122相切于位于K点正上方的曲面K S；
所述P点为切点，P点的坐标取决于K点的y坐标；接触力F的方向为从曲面K S中心指向P点；P点的运动学表示为如下：
P＝[-r ccosθ,r scosβ+r csinθ+D/2,r s-r ssinβ] T
其中，r s是曲面K S的半径，β是接触力F与y轴正方向的夹角。
优选地，所述P随着θ的变化而变化，P点的变化引起形状感知应变片的状态变量B发生改变，状态变量B的定义如下所示：
B＝[L,F,β] T
其中，L表示从H点到P点沿着梁方向的长度，L为形状感知应变片的有效长度；F表示接触力的大小；
所述状态变量B含有三个未知量，需建立三组约束关系来对三个未知量进行求解；α为形状感知应变片122的偏转角，形状感知应变片122与曲面K S的相切关系，得到第一组约束关系为：
α＝β。
优选地，所述a和b分别表示梁在y和z轴上的投影：
a＝[γ 1sinθ p,1+γ 2sin(θ p,1+θ p,2)+γ 3sin(θ p,1+θ p,2+θ p,3)]L
b＝[γ 0+γ 1cosθ p,1+γ 2cos(θ p,1+θ p,2)+γ 3cos(θ p,1+θ p,2+θ p,3)]L
其中，γ i表示第i个伪刚体特征参数，θ p,i表示第i个伪刚体关节角。
优选地，所述固定点H的坐标为[0,H y,H z] T；P的y，z坐标用伪刚体参数表示为：
P y＝H y+a
P z＝H z-b；
将P＝[-r ccosθ,r scosβ+r csinθ+D/2,r s-r ssinβ] T代入
Figure PCTCN2021105090-appb-000001
得到另 外两组约束方程：
r scosβ+r csinθ+D/2＝H y+a
r s-r ssinβ＝H z-b；
将三组约束关系与伪刚体的静力学模型联立，状态变量B通过以下方程进行求解：
α＝β
r s-r ssinβ＝H z-b
r scosβ+r csinθ+D/2＝H y+a
Figure PCTCN2021105090-appb-000002
其中，k i是伪刚体关节的刚度系数，F y和F z表示接触力F在y轴和z轴上的投影；J T是由伪刚体参数表示的雅克比矩阵。
优选地，总的所述FBG偏转角度
Figure PCTCN2021105090-appb-000003
通过下式求解：
Figure PCTCN2021105090-appb-000004
其中，M S和M E表示FBG的起始节点和终止节点，起始节点表示距离H最近的节点，终止节点表示最远的点；M S和M E取决于n，l，L和d；当n足够大时，也就是δL＝L/n<<l时，M S和M E为如下所示：
Figure PCTCN2021105090-appb-000005
Figure PCTCN2021105090-appb-000006
FBG的应变ε通过得到的偏转角度
Figure PCTCN2021105090-appb-000007
进行求解；FBG125安装在应变片的凹槽内，定义FBG的中心线与梁的中心线的距离为h；FBG的应变表示为如下所示：
ε＝h/κ；
其中，
Figure PCTCN2021105090-appb-000008
是FBG的曲率半径。
优选地，当满足相位匹配条件时，光栅的布拉格波长为：
λ＝2n effΛ；
其中，n eff是光线传播模式的有效折射率；Λ为光栅周期；波长的变化量Δλ由应变ε和温度T决定，其关系为：
Figure PCTCN2021105090-appb-000009
其中，ρ α是光纤材料的弹光系数；λ 0是中心波长；ΔT是温度的变化量。
优选地，当应变ε为0，将温度补偿FBG的波长变化代入应变FBG得到：
Figure PCTCN2021105090-appb-000010
其中，Δλ T是温度补偿FBG的波长变化量；上标i表示第i个应变FBG的参数值。
与现有技术相比，本发明具有如下的有益效果：
1、本发明通过采用偏心轮与形状感知应变片配合的结构，将转轴的旋转角度转换为形状感知应变片的形变；解决了传统基于FBG的检测方法的测量范围太小，无法检测360°旋转角度的问题；并且，该结构可用磁安全的材料如：树脂/PMMA等进行装配，从而实现磁共振安全的特性；
2、本发明在实现该检测方法的建模方面，通过采用伪刚体的建模方法并引入3组约束关系，解决了梁的长度可变情况下传统积分方法难以求解梁的状态变量的问题，从而实现旋转角度到FBG波长变化的映射；经过实验表明，该装置的总体检测精度为1.6°；均方根误差为0.46°。
附图说明
通过阅读参照以下附图对非限制性实施例所作的详细描述，本发明的其它特征、目的和优点将会变得更明显：
图1为本发明的整体结构图；
图2为本发明的FBG形状感知应变片结构图；
图3为本发明的形状感知应变片与偏心轮的接触方式图；
图4为本发明的偏心轮与形状感知应变片的几何关系示意图；
图5为本发明的形状感知应变片的伪刚体模型示意图；
图6为本发明的链式算法节点分割图；
图7本发明的FBG检测原理图。
其中：
Figure PCTCN2021105090-appb-000011
Figure PCTCN2021105090-appb-000012
具体实施方式
下面结合具体实施例对本发明进行详细说明。以下实施例将有助于本领域的技术人员进一步理解本发明，但不以任何形式限制本发明。应当指出的是，对本领域的普通技术人员来说，在不脱离本发明构思的前提下，还可以做出若干变化和改进。这些都属于本发明的保护范围。
图1表示该角度传感器的整体结构图。将旋转轴101与待测物连接，通过旋转轴101的旋转来带动偏心轮121的旋转。两个陶瓷轴承102安装在轴套111的两侧，用以保证旋转轴101的稳定性。组装后，两个形状感知应变片122与偏心轮121的边缘相接触。因此，当轴101旋转时，接触点将会发生变化，进而形状感知应变片122的应变大小会随之发生改变。将光纤布拉格光栅传感器124安装于形状感知应变片122中间，当形状感知应变片122的发生偏转时，传感器124同步发生应变，此时传感器检测到的光的波长将会发生变化。形状感知应变片122与偏心轮121的接触关系可以有多种形式，如图3所示，一种垂直接触，一种切向接触。形状感知应变片122及温度补偿应变片123安装与楔形槽104内，通过固定楔子103进行固定。光纤124经过后盖114穿过套管105与外部光栅解调器相连接。
根据偏心轮121的几何结构，当轴101发生旋转时，形状感知应变片122与偏心轮121的接触点P的运动轨迹可近似为正弦曲线。由于正弦曲线在一个周期内的任意一个幅值对应两个旋转角度，该幅值与形状感知应变片122的应变大小相一致。因此，至少需要检测两个不同位置的形状感知应变片122的应变大小来确定当前的旋转角度。本发明采用120°的分布方式设计这两个形状感知应变片之间的相对位置关系，其他形状感知应变片的位置关系或者安装两个以上形状感知应变片也与该发明所提出的想法相一致。另一方面，光纤布拉格光栅传感器124对温度极其敏感，为了补偿因为温度变化而导致的传感器数值变化，设计一个不与偏心轮接触的温度补偿应变片123与另外两个形 状感知应变片122呈120°间隔的圆周分布关系，方向与轴向一致。根据匹配算法，检测到的两个形状感知应变片122内的传感器124波长值可与轴的旋转角度一一对应。形状感知应变片的应变检测方式也可以采用压电传感器或其他可检测梁的形变的传感器。
整体的建模思路如下所示：首先建立轴101的旋转角θ与P点坐标(形状感知应变片122与偏心轮121的接触点)的几何关系；其次，采用三关节伪刚体模型(PRB 3R)建立P点坐标与形状感知应变片122的状态变量B之间的关系；再采用链式算法求解安装在形状感知应变片122特定位置的布拉格光栅(FBG)125的应变；最后，由FBG125的波长与应变的关系，可得经过温度补偿后的采集波长与实际形状感知应变片122的应变之间的关系。通过以上建立的模型，设计相应的匹配算法用于最终的角度检测。
图4表示的是偏心轮121与形状感知应变片122之间的几何关系。根据坐标定义关系，偏心轮在xoy平面上旋转，如图4(a)所示。K是偏心轮的xoy平面沿着y轴方向与原点O距离最远的点。当偏心轮旋转θ时，K沿着圆形轨迹移动到K'点，该轨迹与偏心轮121的中心Q的移动轨迹一致。因此，K的运动学可以表示为如下：
K＝[-r ccosθ,r csinθ+D/2,0] T  (1)
其中，r c是偏心半径，D是偏心轮的直径。
定义两个最远点K r和K l分别表示K点的运动轨迹中的x坐标绝对值最大的两个点。K r表示x坐标为负数的点，K l表示x坐标为正数的点。通过设计形状感知应变片122的宽度w大于K r和K l之间的距离，并且形状感知应变片的扭转可忽略不计，由此假设形状感知应变片122始终相切于位于K点正上方的曲面K S。定义P点为切点，如图4(b)所示。因此，P点的坐标取决于K点的y坐标。另一方面，根据图4(c)所示的相切关系，接触力F的方向始终为从曲面K S(半圆形曲面)中心指向P点。因此，P点的运动学可以表示为如下：
P＝[-r ccosθ,r scosβ+r csinθ+D/2,r s-r ssinβ] T  (2)
其中，r s是曲面K S的半径，β是接触力F与y轴正方向的夹角。公式(2)可以看出，P随着θ的变化而变化，而P点的变化会引起形状感知应变片的状态变量B发生改变，状态变量B的定义如下所示：
B＝[L,F,β] T  (3)
其中，L表示从图4(b)中的H点到P点沿着梁方向的长度，为形状感知应变片的有效长度。F表示接触力的大小。FBG安装于图4(b)所示的点M处，它的长度为l。d表 示H点沿着梁到M点的距离。传统的梁理论大多用于分析L确定的梁状态，而本模型中的L是变量，因此难以直接采用传统梁理论求解FBG所在位置M的应变。本发明将该问题分解成两个步骤：1)首先采用三关节伪刚体模型建立状态变量B与P的对应关系；2)采用链式算法求解应变值。
在梁的状态变量B未知的情况下，传统的积分方法很难求解。因为传统方法所建立的方程含有复杂的积分项或者大量的迭代运算。伪刚体方法通过将梁离散成多个关节，可以大大简化该问题。由于本发明的形状感知应变片是大变形梁，因此选用三关节伪刚体模型对其进行求解。图5表示形状感知应变片122的三关节伪刚体模型。
由于状态变量B含有三个未知量，因此需要建立三组约束关系来对其进行求解。定义α为形状感知应变片122的偏转角，如图5所示。由于形状感知应变片122与曲面K S的相切关系，可以得到第一组约束关系为：
α＝β  (4)
定义a和b分别为梁在y和z轴上的投影：
a＝[γ 1sinθ p,1+γ 2sin(θ p,1+θ p,2)+γ 3sin(θ p,1+θ p,2+θ p,3)]L
b＝[γ 0+γ 1cosθ p,1+γ 2cos(θ p,1+θ p,2)+γ 3cos(θ p,1+θ p,2+θ p,3)]L  (5)
其中，γ i表示第i个伪刚体特征参数，θ p,i表示第i个伪刚体关节角。固定点H的坐标为[0,Hy,Hz]T。因此，P的y，z坐标可以用伪刚体参数表示为如下所示：
P y＝H y+a
P z＝H z-b  (6)
将(2)代入(6)可得另外两组约束方程如下所示：
r scosβ+r csinθ+D/2＝H y+a
r s-r ssinβ＝H z-b   (7)
将三组约束关系与伪刚体的静力学模型联立，状态变量B可以通过以下方程进行求解：
Figure PCTCN2021105090-appb-000013
其中，k i是伪刚体关节的刚度系数，F y和F z表示接触力F在y轴和z轴上的投影。J T是由伪刚体参数表示的雅克比矩阵。由于(8)包含多种正弦函数，因此难以直接得到解析解。采用MATLAB数值求解算法“fsolve”对该问题进行求解。
为了获得FBG的应变，首先需要根据梁的状态变量B求解M处的偏转角
Figure PCTCN2021105090-appb-000014
采用链式算法对该问题进行求解，它的求解思想与有限元类似，但链式算法拥有更快的求解速度。因此链式算法更加适用于本问题中状态变量B不断变化的情况。图6表示链式算法的几何结构图。将形状感知应变片的有效长度离散成n个等长的小节。公式(8)计算出状态变量B的值后，根据链式算法可以得到第i个小节的偏转角度σ i。
因此，总的FBG偏转角度
Figure PCTCN2021105090-appb-000015
可以通过下式求解：
Figure PCTCN2021105090-appb-000016
其中，M S和M E表示FBG的起始节点和终止节点，起始节点表示距离H最近的节点，反之，终止节点表示最远的点。M S和M E取决于n，l，L和d。当n足够大时，也就是δL＝L/n<<l时，M S和M E可以近似为如下所示：
Figure PCTCN2021105090-appb-000017
因此，FBG的应变ε可以通过(9)求解得到的偏转角度
Figure PCTCN2021105090-appb-000018
进行求解。图7(a)表示为FBG的应变示意图。因为作用在梁上的力为侧面接触力，因此可以忽略形状感知应变片轴向的力。因此可以假设形状感知应变片的中心线长度不变。如图7(a)所示，FBG125安装在形状感知应变片的凹槽内，定义FBG的中心线与梁的中心线的距离为h。因此，FBG的应变可以表示为如下所示：
ε＝h/κ  (11)
其中，
Figure PCTCN2021105090-appb-000019
是FBG的曲率半径。
由耦合波理论可得，当满足相位匹配条件时，光栅的布拉格波长为：
λ＝2n effΛ  (12)
其中，n eff是光线传播模式的有效折射率；Λ为光栅周期。波长的变化量Δλ由应变ε和温度T决定，其关系为：
Figure PCTCN2021105090-appb-000020
其中，ρ α是光纤材料的弹光系数，它的取值为0.216；λ 0是中心波长，它对应光纤处于伸直状态下的反射波长；ΔT是温度的变化量。
对于温度补偿FBG，它只受到温度的影响，不受到外力作用，因此在公式(13)中的应变ε为0，将温度补偿FBG的波长变化代入应变FBG可得：
Figure PCTCN2021105090-appb-000021
其中，Δλ T是温度补偿FBG的波长变化量；上标i表示第i个应变FBG的参数值，这两个FBG有着120°的相位差，因此这两者的波长与轴的旋转角之间的关系曲线如图7(b)所示。
最终，通过FBG调制解调仪检测对应的波长数据，并通过图7(b)所示的波长与角度的映射关系，轴的旋转角θ可以被唯一确定。
本发明通过采用偏心轮与形状感知应变片配合的结构，将转轴的旋转角度转换为形状感知应变片的形变；解决了传统基于FBG的检测方法的测量范围太小，无法检测360°旋转角度的问题；并且，该结构可用磁安全的材料如：树脂/PMMA等进行装配，从而实现磁共振安全的特性。
本发明在实现该检测方法的建模方面，通过采用伪刚体的建模方法并引入3组约束关系，解决了梁的长度可变情况下传统积分方法难以求解梁的状态变量的问题，从而实现旋转角度到FBG波长变化的映射；经过实验表明，该装置的总体检测精度为1.6°；均方根误差为0.46°。
本领域技术人员知道，除了以纯计算机可读程序代码方式实现本发明提供的系统及其各个装置、模块、单元以外，完全可以通过将方法步骤进行逻辑编程来使得本发明提供的系统及其各个装置、模块、单元以逻辑门、开关、专用集成电路、可编程逻辑控制器以及嵌入式微控制器等的形式来实现相同功能。所以，本发明提供的系统及其各项装 置、模块、单元可以被认为是一种硬件部件，而对其内包括的用于实现各种功能的装置、模块、单元也可以视为硬件部件内的结构；也可以将用于实现各种功能的装置、模块、单元视为既可以是实现方法的软件模块又可以是硬件部件内的结构。
以上对本发明的具体实施例进行了描述。需要理解的是，本发明并不局限于上述特定实施方式，本领域技术人员可以在权利要求的范围内做出各种变化或修改，这并不影响本发明的实质内容。在不冲突的情况下，本申请的实施例和实施例中的特征可以任意相互组合。

Claims (10)

  1. 一种磁共振安全的旋转编码器，其特征在于，包括旋转轴(101)、偏心轮(121)、轴承(102)、轴套(111)、形状感知应变片(122)、光纤布拉格光栅传感器(124)、温度补偿应变片(123)、楔形槽(104)、固定楔子(103)、后盖(114)和套管(105)；
    所述旋转轴(101)与待测物相连接；所述偏心轮(121)穿设在旋转轴(101)尾端，并由旋转轴(101)带动偏心轮(121)旋转；
    所述轴承(102)安装在轴套(111)的两侧；所述轴套(111)穿设在旋转轴(101)上；
    所述形状感知应变片(122)与偏心轮(121)接触设置，且所述形状感知应变片(122)和温度补偿应变片(123)安装在楔形槽(104)，所述固定楔子(103)用于固定形状感知应变片(122)和温度补偿应变片(123)；
    所述光纤布拉格光栅传感器(124)安装在形状感知应变片(122)上，所述光纤布拉格光栅传感器(124)上的光纤经过后盖(114)穿过套管(105)与外部光栅解调器相连接；
    所述旋转轴(101)发生旋转，形状感知应变片(122)与偏心轮(121)的接触点的运动轨迹近似为正弦曲线。
  2. 一种磁共振安全的旋转编码器的旋转角度检测方法，其特征在于，所述方法包括权利要求1中所述的一种磁共振安全的旋转编码器，所述方法包括如下步骤：
    步骤1：建立旋转轴的旋转角θ与形状感知应变片122与偏心轮121的接触点P点坐标的几何关系；
    步骤2：采用三关节伪刚体模型PRB 3R建立P点坐标与形状感知应变片122的状态变量B之间的关系；
    步骤3：采用链式算法求解安装在形状感知应变片122上的布拉格光栅125的应变；
    步骤4：由布拉格光栅125的波长与应变的关系，得到经过温度补偿后的采集波长与实际形状感知应变片122的应变之间的关系；
    步骤5：通过步骤1-4建立的模型，设计相应的匹配算法用于最终的角度检测。
  3. 根据权利要求2所述的一种磁共振安全的旋转编码器的旋转角度检测方法，其特征在于，所述偏心轮在xoy平面上旋转，K是偏心轮的xoy平面沿着y轴方向与原点O距离最远的点；当偏心轮旋转θ时，K沿着圆形轨迹移动到K'点，该轨迹与 偏心轮121的中心Q的移动轨迹一致；K的运动学表示为如下：
    K＝[-r ccosθ,r csinθ+D/2,0] T
    其中，r c是偏心半径，D是偏心轮的直径；
    所述K r和K l分别表示K点的运动轨迹中的x坐标绝对值最大的两个点；K r表示x坐标为负数的点，K l表示x坐标为正数的点。
  4. 根据权利要求1所述的一种磁共振安全的旋转编码器的旋转角度检测方法，其特征在于，所述形状感知应变片122的宽度w大于K r和K l之间的距离，形状感知应变片122相切于位于K点正上方的曲面K S；
    所述P点为切点，P点的坐标取决于K点的y坐标；接触力F的方向为从曲面K S中心指向P点；P点的运动学表示为如下：
    P＝[-r ccosθ,r scosβ+r csinθ+D/2,r s-r ssinβ] T
    其中，r s是曲面K S的半径，β是接触力F与y轴正方向的夹角。
  5. 根据权利要求1所述的一种磁共振安全的旋转编码器的旋转角度检测方法，其特征在于，所述P随着θ的变化而变化，P点的变化引起形状感知应变片的状态变量B发生改变，状态变量B的定义如下所示：
    B＝[L,F,β] T
    其中，L表示从H点到P点沿着梁方向的长度，L为形状感知应变片的有效长度；F表示接触力的大小；
    所述状态变量B含有三个未知量，需建立三组约束关系来对三个未知量进行求解；α为形状感知应变片122的偏转角，形状感知应变片122与曲面K S的相切关系，得到第一组约束关系为：
    α＝β。
  6. 根据权利要求1所述的一种磁共振安全的旋转编码器的旋转角度检测方法，其特征在于，所述a和b分别表示梁在y和z轴上的投影：
    a＝[γ 1sinθ p,1+γ 2sin(θ p,1+θ p,2)+γ 3sin(θ p,1+θ p,2+θ p,3)]L
    b＝[γ 0+γ 1cosθ p,1+γ 2cos(θ p,1+θ p,2)+γ 3cos(θ p,1+θ p,2+θ p,3)]L
    其中，γ i表示第i个伪刚体特征参数，θ p,i表示第i个伪刚体关节角。
  7. 根据权利要求1所述的一种磁共振安全的旋转编码器的旋转角度检测方法，其特征在于，所述固定点H的坐标为[0,H y,H z] T；P的y，z坐标用伪刚体参数表示为：
    P y＝H y+a
    P z＝H z-b；
    将P＝[-r ccosθ,r scosβ+r csinθ+D/2,r s-r ssinβ] T代入
    Figure PCTCN2021105090-appb-100001
    得到另外两组约束方程：
    r scosβ+r csinθ+D/2＝H y+a
    r s-r ssinβ＝H z-b；
    将三组约束关系与伪刚体的静力学模型联立，状态变量B通过以下方程进行求解：
    α＝β
    r s-r ssinβ＝H z-b
    r scosβ+r csinθ+D/2＝H y+a
    Figure PCTCN2021105090-appb-100002
    其中，k i是伪刚体关节的刚度系数，F y和F z表示接触力F在y轴和z轴上的投影；J T是由伪刚体参数表示的雅克比矩阵。
  8. 根据权利要求1所述的一种磁共振安全的旋转编码器的旋转角度检测方法，其特征在于，总的所述FBG偏转角度
    Figure PCTCN2021105090-appb-100003
    通过下式求解：
    Figure PCTCN2021105090-appb-100004
    其中，M S和M E表示FBG的起始节点和终止节点，起始节点表示距离H最近的节点，终止节点表示最远的点；M S和M E取决于n，l，L和d；当n足够大时，也就是δL＝L/n<<l时，M S和M E为如下所示：
    Figure PCTCN2021105090-appb-100005
    Figure PCTCN2021105090-appb-100006
    FBG的应变ε通过得到的偏转角度
    Figure PCTCN2021105090-appb-100007
    进行求解；FBG125安装在应变片的凹槽内，定义FBG的中心线与梁的中心线的距离为h；FBG的应变表示为如下所示：
    ε＝h/κ；
    其中，
    Figure PCTCN2021105090-appb-100008
    是FBG的曲率半径。
  9. 根据权利要求1所述的一种磁共振安全的旋转编码器的旋转角度检测方法，其特征在于，当满足相位匹配条件时，光栅的布拉格波长为：
    λ＝2n effΛ；
    其中，n eff是光线传播模式的有效折射率；Λ为光栅周期；波长的变化量Δλ由应变ε和温度T决定，其关系为：
    Figure PCTCN2021105090-appb-100009
    其中，ρ α是光纤材料的弹光系数；λ 0是中心波长；ΔT是温度的变化量。
  10. 根据权利要求9所述的一种磁共振安全的旋转编码器的旋转角度检测方法，其特征在于，当应变ε为0，将温度补偿FBG的波长变化代入应变FBG得到：
    Figure PCTCN2021105090-appb-100010
    其中，Δλ T是温度补偿FBG的波长变化量；上标i表示第i个应变FBG的参数值。
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